In battle Normalize makes all moves used by the Pokémon with this Ability act Normal-type instead of its ordinary typing.
All moves. Hidden Power is no exception; I don't see why it would be.
Because of this, a pure Normal-type Pokémon will never receive same-type attack bonus when using Hidden Power unless it also has Normalize as its Ability.
This is the only way a Normal Pokemon can receive STAB from HP. HP cannot be Normal type except for the Normalise ability, despite it being classed as Normal type in game.
Normalise
Hidden Power
Yes it does
Source: I just tested it on Showdown with JamesBlob.
My Delcatty used Hidden Power [Ghost] on Blob's Gastly, and Gastly was immune to it, meaning that Normalize made it a normal type move, otherwise it would have been Super Effective.